The paper proposes a new nonparametric prior for twodimensional vectors of survival functions (S1, S2). The definition we introduce is based on the notion of L´evy copula and it will be used to model, in a nonparametric Bayesian framework, twosample survival data. Such an application will yield a natural extension of the more familiar neutral to the right process of Doksum (1974) adopted for drawing inferences on single survival functions. We, then, obtain a description of the posterior distribution of (S1, S2), conditionally on possibly rightcensored data. As a byproduct of our analysis, we find out that the marginal distribution of a pair of observations from the two samples coincides with the MarshallOlkin or the Weibull distribution according to specific choices of the marginal L´evy measures.